Preheat your oven to 375°F (190°C). Begin by blanching the broccoli florets in boiling water for 2 minutes, then immediately plunge them into ice water. Drain well and set aside.

In a large skillet, melt 2 tablespoons of butter over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes. Stir in the minced garlic and cook for another minute until aromatic.

Sprinkle the flour over the onion and garlic mixture, stirring constantly to cook off the raw flour taste, about 1-2 minutes.

Gradually whisk in the milk, ensuring there are no lumps. Continue to cook, stirring frequently, until the sauce thickens enough to coat the back of a spoon, about 5-7 minutes.

Reduce the heat to low and stir in the shredded cheddar cheese and cream cheese until melted and smooth. Season with smoked paprika, dried thyme, salt, and pepper.

Add the blanched broccoli and corn to the cheese sauce, gently folding them in to ensure they're evenly coated.

Transfer the mixture to a greased 9x13 inch baking dish. In a small bowl, melt the remaining 1 tablespoon of butter and mix with the panko breadcrumbs. Sprinkle this mixture evenly over the top of the casserole.

Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and the sauce is bubbling around the edges. Let the casserole sit for 5 minutes before serving.